The magnitude of lift forces acting on drops and bubbles in liquids flowing inside microchannels

Hydrodynamic lift forces offer a convenient way to manipulate particles in microfluidic applications, but there is little quantitative information on how non-inertial lift mechanisms act and compete with each other in the confined space of microfluidic channels. This paper reports measurements of lift forces on nearly spherical drops and bubbles, with diameters from one quarter to one half of the width of the channel, flowing in microfluidic channels, under flow conditions characterized by particle capillary numbers Ca(P) = 0.0003-0.3 and particle Reynolds numbers Re(P) = 0.0001-0.1. For Ca(P) < 0.01 and Re(P) < 0.01 the measured lift forces were much larger than predictions of deformation-induced and inertial lift forces found in the literature, probably due to physicochemical hydrodynamic effects at the interface of drops and bubbles, such as the presence of surfactants. The measured forces could be fit with good accuracy using an empirical formula given herein. The empirical formula describes the power-law dependence of the lift force on hydrodynamic parameters (velocity and viscosity of the carrier phase; sizes of channel and drop or bubble), and includes a numerical lift coefficient that depends on the fluids used. The empirical formula using an average lift coefficient of ~500 predicted, within one order of magnitude, all lift force measurements in channels with cross-sectional dimensions below 1 mm.